75.12.23 problem 297

Internal problem ID [16889]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 297
Date solved : Tuesday, January 28, 2025 at 09:39:49 AM
CAS classification : [_separable]

\begin{align*} \left (x -1\right ) \left (y^{2}-y+1\right )&=\left (y-1\right ) \left (x^{2}+x +1\right ) y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 1.211 (sec). Leaf size: 2397

dsolve(((x-1)*(y(x)^2-y(x)+1))=((y(x)-1)*(x^2+x+1))*diff(y(x),x),y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

✓ Solution by Mathematica

Time used: 0.425 (sec). Leaf size: 77

DSolve[((x-1)*(y[x]^2-y[x]+1))==((y[x]-1)*(x^2+x+1))*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {K[1]-1}{K[1]^2-K[1]+1}dK[1]\&\right ]\left [\int _1^x\frac {K[2]-1}{K[2]^2+K[2]+1}dK[2]+c_1\right ] \\ y(x)\to \sqrt [3]{-1} \\ y(x)\to -(-1)^{2/3} \\ \end{align*}